There are 1 questions in this calculation: for each question, the 2 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ \frac{(x + y)}{({x}^{2} + {y}^{2} + xy)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{x}{(x^{2} + yx + y^{2})} + \frac{y}{(x^{2} + yx + y^{2})}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{x}{(x^{2} + yx + y^{2})} + \frac{y}{(x^{2} + yx + y^{2})}\right)}{dx}\\=&(\frac{-(2x + y + 0)}{(x^{2} + yx + y^{2})^{2}})x + \frac{1}{(x^{2} + yx + y^{2})} + (\frac{-(2x + y + 0)}{(x^{2} + yx + y^{2})^{2}})y + 0\\=&\frac{-2x^{2}}{(x^{2} + yx + y^{2})^{2}} - \frac{3yx}{(x^{2} + yx + y^{2})^{2}} - \frac{y^{2}}{(x^{2} + yx + y^{2})^{2}} + \frac{1}{(x^{2} + yx + y^{2})}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{-2x^{2}}{(x^{2} + yx + y^{2})^{2}} - \frac{3yx}{(x^{2} + yx + y^{2})^{2}} - \frac{y^{2}}{(x^{2} + yx + y^{2})^{2}} + \frac{1}{(x^{2} + yx + y^{2})}\right)}{dx}\\=&-2(\frac{-2(2x + y + 0)}{(x^{2} + yx + y^{2})^{3}})x^{2} - \frac{2*2x}{(x^{2} + yx + y^{2})^{2}} - 3(\frac{-2(2x + y + 0)}{(x^{2} + yx + y^{2})^{3}})yx - \frac{3y}{(x^{2} + yx + y^{2})^{2}} - (\frac{-2(2x + y + 0)}{(x^{2} + yx + y^{2})^{3}})y^{2} + 0 + (\frac{-(2x + y + 0)}{(x^{2} + yx + y^{2})^{2}})\\=&\frac{8x^{3}}{(x^{2} + yx + y^{2})^{3}} + \frac{16yx^{2}}{(x^{2} + yx + y^{2})^{3}} - \frac{6x}{(x^{2} + yx + y^{2})^{2}} + \frac{10y^{2}x}{(x^{2} + yx + y^{2})^{3}} - \frac{4y}{(x^{2} + yx + y^{2})^{2}} + \frac{2y^{3}}{(x^{2} + yx + y^{2})^{3}}\\ \end{split}\end{equation} \]

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